AP Photo/Orlin Wagner

LOS ANGELES—California’s new primary system will undergo a high-profile test on Tuesday, its first for a handful of statewide offices such as governor and its second ever.

The new system — tested first in 2012 — throws open the typical primary process. In most primaries, the top vote-getter from each party proceeds to run in the general election. The downside with that old system in California was that it locked out independents and only allowed registered voters in each party to choose among their own side’s candidates. Under the new top-two primary — sometimes called the jungle or blanket primary — all candidates appear on the ballot and the two with the most overall votes move ahead, regardless of party.

“It changes voter behavior to the extent that you’re not just locked into the voting for whichever member of party you think should get to the general election,” says Jessica Levinson, an election law professor at Loyola University’s law school in Los Angeles and the vice president of the city’s ethics commission.

Voters approved the new system four years ago next Sunday in a 54 percent to 46 percent vote and it went into effect on the first day of 2011. Its application in California represents a high-profile test of a system that only exists in a few other places — Washington and Louisiana held similar primaries.

The hope among some advocates was that since it freed up options to voters, the top-two system might also encourage more of them to show up on election day. But turnout in the 2012 primary was the lowest of any presidential primary in 90 years, according to a May Public Policy Institute of California report.

Of course, primary participation in the Golden State is monstrous in absolute terms. As our The Fix colleague Philip Bump pointed out on Monday, more people turned out in the California primary last year than reside in more than half the states. And California has long been near the top of the heap, even in relative terms, as PPIC pointed out in its report.

(Public Policy Institute of California)

But, according to that same report, similar top-two systems in effect over the past 30 years don’t appear to have boosted turnout much. Turnout seems to be falling and the report’s authors have little expectation that the new system will reverse the trend. But even as the top-two primary doesn’t seem to boost turnout, the reasons behind that are less clear, they write.

Each primary may motivate different types of voters, having a potentially neutralizing effect, they suggest. It’s true that in an open primary a small group of independents has more incentive to vote. But in a closed primary, there are relatively more reliable partisan voters. Turnout under an open primary system also seems to be more volatile, they find — independents appear to be more motivated to vote only if a race is close.

But there’s a bright side. Even if the top-two primary doesn’t seem to significantly boost turnout, its small boost in independent voting means those voters may weigh in more on down-ballot races, the kinds that draw fewer headlines. As a result, overall participation may get a boost. Academics and analysts will be watching Tuesday’s elections closely not only to see whether that’s true, but also how else the new open primary system may effect turnout in the nation’s most populous state.